2 VocabularyMonomial - a number, a variable, or a product of a number and one or more variables. 4x, 20x2yw3, -3, a2b3, and 3yz are all monomials.Polynomial – one or more monomials added or subtracted4x + 6x2, 20xy - 4, and 3a2 - 5a + 4 are all polynomials.
3 Like TermsLike Terms refer to monomials that have the same variable(s) but may have different coefficients. The variables in the terms must have the same powers.Which terms are like? a2b, 4ab2, 3ab, -5ab24ab2 and -5ab2 are like.Even though the others have the same variables, the exponents are not the same.3a2b = 3aab, which is different from 4ab2 = 4abb.
4 Constants are like terms. Which terms are like? x, -3, 5b, 0-3 and 0 are like.Which terms are like? x, 2x2, 4, x3x and x are like.Which terms are like? wx, w, 3x, 4xw2wx and 4xw are like.
5 Adding Polynomials Add: (x2 + 3x + 1) + (4x2 +5) Step 1: Underline like terms:(x2 + 3x + 1) + (4x2 +5)Notice: ‘3x’ doesn’t have a like term.Step 2: Add the coefficients of like terms, do not change the powers of the variables:(x2 + 4x2) + 3x + (1 + 5)5x2 + 3x + 6
6 Adding PolynomialsSome people prefer to add polynomials by stacking them. If you choose to do this, be sure to line up the like terms!(x2 + 3x + 1)+ (4x )(x2 + 3x + 1) + (4x2 +5)5x2 + 3x + 6Stack and add these polynomials: (2a2+3ab+4b2) + (7a2+ab+-2b2)(2a2 + 3ab + 4b2)+ (7a2 + ab + -2b2)(2a2+3ab+4b2) + (7a2+ab+-2b2)9a2 + 4ab + 2b2
7 Adding PolynomialsAdd the following polynomials; you may stack them if you prefer:
8 Subtracting Polynomials Subtract: (3x2 + 2x + 7) - (x2 + x + 4)Step 1: Change subtraction to addition (Keep-Change-Change.).(3x2 + 2x + 7) + (- x2 + - x + - 4)Step 2: Underline OR line up the like terms and add.(3x2 + 2x + 7)+ (- x2 + - x + - 4)2x x + 3
9 Subtracting Polynomials Subtract the following polynomials by changing to addition (Keep-Change-Change.), then add: